Radiative transfer models can be used to model the transfer of electromagnetic radiation (e.g., sunlight) in the atmosphere and can be useful for understanding and modeling phenomena such as global climate change. One factor these models consider is how much light is absorbed or reflected by particles suspended in the atmosphere, thereby contributing to radiative forcing. Such particles include aerosols, which are generally no larger than about 10 μm in diameter. Aerosols may be generated naturally, for example by wild fires, dust entrainment, volcanic eruptions, etc., or they may be a result of human activity, such as the burning of fossil fuels. The amount of light that an aerosol or other particle absorbs or scatters depends on factors such as the size, shape and composition of the particle.
The angular distribution of light scattered by aerosol particles is useful in determining the aerosol contribution to radiative forcing. This angular distribution is commonly parameterized into a single value, the asymmetry parameter g, for use in large-scale radiative transfer models. This asymmetry parameter g is used to describe the angular distribution or phase function of aerosol scattering, often according to the single-parameter Henyey-Greenstein phase function. See, e.g., Henyey, L. C. and J. L. Greenstein “Diffuse Radiation in the Galaxy,” Astrophys. J 93, 70-83 (1941); and Cornette, W. M. and J. G. Shanks, “Physically Reasonable Analytic Expression for the Single-Scattering Phase Function,” Appl. Opt. 31, 3152-3160 (1992). According to this function, the asymmetry parameter g is defined as an intensity-weighted average cosine of the scattering angle,
                                                        g              =                            ⁢                                                1                                      4                    ⁢                    π                                                  ⁢                                                      ∫                                          4                      ⁢                      π                                                        ⁢                                                                          ⁢                                                            ⅆ                      Ω                                        ⁢                                                                                  ⁢                                          P                      ⁡                                              (                        θ                        )                                                              ⁢                                          cos                      ⁡                                              (                        θ                        )                                                                                                                                                                    =                            ⁢                                                1                                      4                    ⁢                    π                                                  ⁢                                                      ∫                    0                    π                                    ⁢                                                                          ⁢                                                            ⅆ                      θ                                        ⁢                                                                                  ⁢                                          P                      ⁡                                              (                        θ                        )                                                              ⁢                                          sin                      ⁡                                              (                        θ                        )                                                              ⁢                                          cos                      ⁡                                              (                        θ                        )                                                              ⁢                                                                  ∫                        0                                                  2                          ⁢                          π                                                                    ⁢                                                                                          ⁢                                              ⅆ                        ϕ                                                                                                                                                                                    =                                ⁢                                                      1                    2                                    ⁢                                                            ∫                      0                      π                                        ⁢                                                                                  ⁢                                                                  ⅆ                        θ                                            ⁢                                                                                          ⁢                                              P                        ⁡                                                  (                          θ                          )                                                                    ⁢                                              sin                        ⁡                                                  (                          θ                          )                                                                    ⁢                                              cos                        ⁡                                                  (                          θ                          )                                                                                                                                ,                                                          (        1        )            wherein θ is an angle between a propagation direction of an incident light flux and a direction of propagation of a scattered light flux, and wherein P(θ) is a phase function giving an angular distribution of the scattered light. Values of g range from −1 for pure backscattering to +1 for pure forward scattering.
Rather than being measured directly, the asymmetry parameter g is typically estimated indirectly from other aerosol parameters. See, e.g., Andrews et al., “Comparison of Methods for Deriving Aerosol Asymmetry Parameter,” J. Geophys. Res., 111, doi: 10.1029/2004JD005734 (2006). Cloud integrating nephelometers and polar nephelometers have been used for the measurement of g for large particles (e.g., large relative to the wavelength of incident light that the particles scatter), including water drops and ice crystals. Modifications to an integrating nephelometer to measure aerosol g directly have been proposed previously. See, e.g., Gayet, J. F. et al. “A New Airborne Polar Nephelometer for the Measurements of Optical and Microphysical Cloud Properties. Part I: Theoretical Design” Ann. Geophysicae 15, 451-459 (1997); Gerber et al. “Nephelometer Measurements of the Asymmetry Parameter, Volume Extinction Coefficient, and Backscatter Ratio in Arctic Clouds,” J. Atmos. Sci. 57, 3021-3034 (2000); and Heintzenberg, J. and R. J. Charlson, “Design and Application of the Integrating Nephelometer: A Review,” J. Atmos. Ocean. Technol. 13, 987-1000 (1996). Cloud integrating nephelometers typically cannot measure aerosol properties, and polar nephelometers are typically complex and expensive.